I've found that while many things - especially ATH, SPD, and BH - tend to help improve the numbers, the PER rating seems by far the biggest predictor of success for any individual player with regard to scoring from three point range.
I've had guys with somewhat limited ATH, SPD, and BH at DIII who have still lit it up for an entire season from beyond the arc.
For example,
this guy is rather pedestrian (by my standards) in terms of ATH and SPD and his BH is passable but not what I'd really like it to be, and yet he was incredibly productive coming off my bench and scoring from three point land last season as a freshman.